Determinism is the position that every event is caused, the inevitable and necessary consequence of antecedent events, in a chain of events with just one possible future.

"Hard" and "soft" determinism are terms invented by William James, who lamented the fact that some determinists were co-opting the term freedom for themselves. He called them "soft" determinists, because, abhoring harsh words like fatality, necessity, and even predetermination, they say determinism’s "real name is freedom; for freedom is only necessity understood, and bondage to the highest is identical with true freedom."

Hard incompatibilists think both free will and moral responsibility are not compatible with determinism (they mean pre-determinism).

Illusionists are hard incompatibilists, who say that free will is an illusion. They usually deny moral responsibility, but some say we can preserve responsibility by maintaining the illusion.

Impossibilists are also hard incompatibilists. They say moral responsibility is impossible.

Incompatibilism is the idea that free will and determinism are incompatible. Incompatibilists include both hard determinists and libertarians. Incompatibilists include both hard determinists and libertarians (both yellow in the taxonomy). This confuses the debate by analytic language philosophers - who are normally committed to clear and unambiguous concepts - and adds difficulties for students of philosophy.

Soft incompatibilists says that free will is incompatible with pre-determinism, and that pre-determinism is not true. Using "soft" is preferable to the loose usage of the term "incompatibilist" to describe a libertarian, since "incompatibilist" is ambiguous and also used for determinists, the "hard" incompatibilists.

Indeterminism is the position that there are random (chance) events in a world of possible futures. The irreducible indeterminism is quantum indeterminacy.

Libertarians believe that indeterminism makes free will possible. Note that there many philosophers who admit indeterminism may be true but that it does not really explain free will ("hard" indeterminists?). See the standard argument against free will - If our actions are determined, we are not free. If they are random, we are not responsible for them. So indeterminism is not enough. We need a limited indeterminism in the first stage and also "adequate determinism" in the second stage of a two-stage model.

Agent-causal indeterminists are libertarians who think that agents have originating causes for their actions that are not events. Actions do not depend on any prior causes. Some call this "metaphysical" freedom.

Event-causal indeterminists generally accept the view that random events (most likely quantum mechanical events) occur in the world. Whether in the physical world, in the biological world (where they are a key driver of genetic mutations), or in the mind, randomness and uncaused events are real. They introduce the possibility of accidents, novelty, and human creativity.

Soft Causality is the idea that most events are adequately determined by normal causes, but that some events are not precisely predictable from prior events, because there are occasional quantum events that start new causal chains with unpredictable futures. These events are said to be causa sui.

While microscopic quantum events are powerful enough to deny strict determinism, the magnitude of these events is generally so small, especially for large macroscopic objects, that the world is still overwhelmingly deterministic. We call this "adequate determinism."

Although random quantum mechanical events break the strictly deterministic causal chain, which has just one possible future, random events are probable causes for later events. They start new causal chains with unpredictable futures. They are said to be causa sui. They need not be the direct cause of human actions, which would make the actions random, but simply provide alternative possibilities for willed actions.